A lower bound for the job insertion problem

Authors:
Tamás Kis;Alain Hertz
Affiliations:
Computer and Automation Research Institute, Hungarian Academy of Sciences, Kende utca 13-17, H-1111 Budapest, Hungary;Département de Mathématiques et de Génie Industriel, Ecole Polytechnique, CP 6079, succ., Centre-ville, Montreal (QC), Canada H3C 3A7
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

This note deals with the job insertion problem in job-shop scheduling: Given a feasible schedule of n jobs and a new job which is not scheduled, the problem is to find a feasible insertion of the new job into the schedule which minimises the makespan. Since the problem is NP-hard, a relaxation method is proposed to compute a strong lower bound. Conditions under which the relaxation provides us with the makespan of the optimal insertion are derived. After the analysis of the polytope of feasible insertions, a polynomial time procedure is proposed to solve the relaxed problem. Our results are based on the theory of perfect graphs and elements of polyhedral theory.